The Exact Circuit Complexity of Boolean Functions in an Infinite Basis

The exact value of the complexity of the circuit implementation of an arbitrary Boolean function in a certain basis consisting of negation and all monotone Boolean functions is found. The complexity of a function is defined as the least number of basis elements sufficient to construct a circuit implementation of this function.

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Publication Details

Journal
Mathematical Notes
Published
2025-04-01
DOI
https://doi.org/10.1134/s0001434625030241
Primary Topic
Machine Learning and Algorithms
Type
article
Field-Weighted Citation Impact
0.00
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article

The Exact Circuit Complexity of Boolean Functions in an Infinite Basis

V. V. Kochergin, A. V. Mikhailovich
Mathematical Notes
Machine Learning and Algorithms
article

The Exact Circuit Complexity of Boolean Functions in an Infinite Basis

V. V. Kochergin, A. V. Mikhailovich
article en

Abstract

The exact value of the complexity of the circuit implementation of an arbitrary Boolean function in a certain basis consisting of negation and all monotone Boolean functions is found. The complexity of a function is defined as the least number of basis elements sufficient to construct a circuit implementation of this function.

Mathematical NotesVol. 117(3-4)
National Research University Higher School of Economics (RU), Lomonosov Moscow State University (RU)
Openalex Percentile: Top 93%
Machine Learning and Algorithms
DOISourceOpenAlex
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The Exact Circuit Complexity of Boolean Functions in an Infinite Basis — V. V. Kochergin, A. V. Mikhailovich · Mathematical Notes (2025) | TGRS Research Map | TGRS